First this really is not the most up to date info on the subject (the website cited is from "Last Modified: Sunday, September 26, 1999"). So I wouldn't get all upset and think things are moving quickly on this. Changing from the greenback would cause all kinds of problems for politicians so don't think that they are about to go getting rid of the US dollar. That said there are a lot of huge benefits for currency union (as well as some drawbacks).
Walker you asked about this, one of the issues with currencies is flucutations in exchange rate that cause a huge cost of doing business. If currencies are pegged (as is China's is right now to the US dollar) you know at the begining of a transaction what it will cost you and there is not a lot of risk. If however you are manufacturing your goods in Mexico and the exchange rate changes between the peso and US dollar in a way that went against your transaction you could lose a lot (they actually buy futures to insure against this kind of loss, but what that means is a transaction cost to doing business in Mexico or Canada, or anywhere else for that manner). So really the general reason isn't so you can go shopping up in Canada or on vacation w/out changing notes.
As for the Amero itself, while Bush has been behind the idea, it would almost be impossible to pass, you'll notice that all the website against the idea are pretty low quality and that there is generally almost no traditional media talk about it, this isn't because there is some conspiracy to get rid of the US dollar. Accomplishing something like this would take time (look to the EU who did this) other countries have and still do lock their rates together and this is definitely something that is possible without actually printing new notes.